The ants are not eating or affecting your lily petals. Some types of lily species and cultivars - but not all - secret nectar to attract insects. Each lily bloom does not hold its petals indefinitely - fresh looking for a few days, likely dropping petals within a week.

Lilies only bloom once a year and don't last very long when open.

There is no way ants are causing your petals to drop prematurely. If they are dropping sooner than normal it is usually a watering issue.

Lilies are very pretty but they are not a plant that will give long lasting color in a pot.

What might have happened here is that your lilies were visited by moths , who pollinated them. Pollinated flowers lose petals very quickly.

In looking at your picture closely, I see the damage you're talking about. Its not ants. Most likely its another tiny little insect which looking for a place to lay its eggs, most likely in the developing seed pod where it knows its larvae will be well nourished. You might try an insect spray made by S.C. Johnson (Johnson Wax) thats safe for indoor house plants. It won't hurt your lily. When your lily is done flowwering, cut the flower head off; leave the stem and leaves to rebuild the bulb for next Spring. Fertilize lightly once and water lightly until it dies back in the fall, then cut off about two inches above surface.